Question

99 POINT QUESTION PLUS BRAINLIEST!!!

Answer 1

First one

limits of inegration are x=5 and 9
$\pi \int\limits^9_5 { (\frac{1}{x})^2 } \, dx$

and $\int\limits^9_5 { (\frac{1}{x})^2 } \, dx= [ \frac{-1}{x}] ^9_5= \frac{4}{45}$ so
$\pi \int\limits^9_5 { (\frac{1}{x})^2 } \, dx = \pi \frac{4}{45}= \frac{\pi 4}{45}$
A is answer





2.
limits are x=0 and 8
$\pi \int\limits^8_0 { (\frac{1}{\sqrt{x+11}})^2 } \, dx$
$\int\limits^8_0 { (\frac{1}{\sqrt{x+11}})^2 } \, dx=\int\limits^8_0 { \frac{1}{x+11} } \, dx=[ln|x+11|]^8_0=ln \frac{19}{11}$ so

$\pi \int\limits^8_0 { (\frac{1}{\sqrt{x+11}})^2 } \, dx= \pi ln \frac{19}{11}$

answer is D